When engine startup and downshifting are processed in parallel while a vehicle is traveling, not only can the time required from the start of downshifting to the end of downshifting be shortened, but downshifting control that prevents draw shock can be easily performed. A control device of an FR hybrid vehicle comprises an engine (Eng), a motor/generator (MG), a first clutch (CL1), an automatic transmission (AT), a second clutch (CL2), and startup/shifting simultaneous processing means ( FIG. 6 ). When engine speed increase control for increasing the engine speed by the motor/generator (MG) in order to start up the engine during travel and downshifting control of the automatic transmission (AT) are processed in parallel, the startup/shifting simultaneous processing means ( FIG. 6 ) uses the motor torque of the motor/generator (MG) to increase the increase of input speed by the downshifting control to a target input speed while engine speed increase control is being performed by the motor/generator (MG).